Theorem relin1

Description: The intersection with a relation is a relation. (Contributed by NM, 16-Aug-1994)

	Ref	Expression
Assertion	relin1	$$⊢\mathrm{Rel}A\to \mathrm{Rel}\left(A\cap B\right)$$

Proof

Step	Hyp	Ref	Expression
1		inss1	$$⊢A\cap B\subseteq A$$
2		relss	$$⊢A\cap B\subseteq A\to \left(\mathrm{Rel}A\to \mathrm{Rel}\left(A\cap B\right)\right)$$
3	1 2	ax-mp	$$⊢\mathrm{Rel}A\to \mathrm{Rel}\left(A\cap B\right)$$